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A145768
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a(n) = the bitwise XOR of squares of first n natural numbers.
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10
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0, 1, 5, 12, 28, 5, 33, 16, 80, 1, 101, 28, 140, 37, 225, 0, 256, 33, 357, 12, 412, 37, 449, 976, 400, 993, 325, 924, 140, 965, 65, 896, 1920, 961, 1861, 908, 1692, 965, 1633, 912, 1488, 833, 1445, 668, 1292, 741, 2721, 512, 2816, 609, 2981, 396, 2844, 485
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OFFSET
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0,3
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COMMENTS
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Up to n=10^8, a(15) is the only zero term and a(1)=a(9) are the only terms for which a(n)=1. Can it be proved that any number can only appear a finite number of times in this sequence? [M. F. Hasler, Oct 20 2008]
If squares occur, they must be at indexes != 2 or 5 (mod 8). - Roderick MacPhee, Jul 17 2017
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LINKS
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FORMULA
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a(n)=1^2 xor 2^2 xor ... xor n^2.
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MAPLE
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A[0]:= 0:
for n from 1 to 100 do A[n]:= Bits:-Xor(A[n-1], n^2) od:
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MATHEMATICA
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Rest@ FoldList[BitXor, 0, Array[#^2 &, 50]]
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PROG
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(PARI) an=0; for( i=1, 50, print1(an=bitxor(an, i^2), ", ")) \\ M. F. Hasler, Oct 20 2008
(PARI) al(n)=local(m); vector(n, k, m=bitxor(m, k^2))
(Haskell)
import Data.Bits (xor)
a145768 n = a145768_list !! n
(Python)
from operator import xor
....return reduce(xor, [x**2 for x in range(n+1)]) # Chai Wah Wu, Aug 08 2014
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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